NEW YORK, March 6 (Reuters) - U.S. stocks eked out a small gain on Tuesday after a choppy session as investors worried about the prospects of a trade war due to mixed signals from Washington on whether U.S. President Donald Trump would follow through with proposed tariffs.

Trump reiterated his plan to slap hefty import tariffs on steel and aluminum saying “trade wars aren’t so bad” even as lawmakers such as Senate Majority Leader Mitch McConnell stepped up calls to scrap the proposal.

Earlier in the day strategists said some investors were beginning to bet Trump would not follow through on the proposal, which they saw as a negotiating tactic in trade talks. But gains were limited by the uncertainty throughout the day.

“The market doesn’t want to hear the uncertainty, the market wants to hear one way or another,” said Chris Zaccarelli, Chief Investment Officer at Independent Advisor Alliance in Charlotte, North Carolina.

“If our worst fears are confirmed ... the market should have even greater losses than what we saw last week. Likewise if it seems we’re not going to have a trade war the market should go higher.”

Jonathan Mackay, investment strategist at Schroders Investment Management in New York, said there are “no winners in a trade war.”

“The market is basically grasping for straws around what the (tariff) policy is going to be. Based on the action we saw today it’s hoping it doesn’t turn into a trade war,” he said.

Investors were also eyeing news that North Korea was open to the possibility of talks with the United States on denuclearization.

“North Korea helps around the margin,” said Mackay.

The Dow Jones Industrial Average rose 9.36 points, or 0.04 percent, to close at 24,884.12, the S&P 500 gained 7.18 points, or 0.26 percent, to 2,728.12 and the Nasdaq Composite added 41.30 points, or 0.56 percent, to 7,372.01.

Most of the S&P’s 11 sectors rose, with the materials index leading the gainers with a 1.1 percent increase as investors in that sector bet against a trade war, according to Independent Advisor Alliance’s Zaccarelli.

Utilities was the biggest faller, with a 1.4 percent drop.

Among the bigger movers of the day, Target fell 4.5 percent after the big-box retailer reported lower-than-expected profit for the holiday quarter.

Qualcomm dropped 2.9 percent after a U.S. government national security panel said it identified potential risks that warrant a full investigation of Broadcom Ltd’s $117-billion bid for the chipmaker.

Advancing issues outnumbered declining ones on the NYSE by a 2.27-to-1 ratio; on Nasdaq, a 1.87-to-1 ratio favored advancers.

The S&P 500 posted 21 new 52-week highs and no new lows; the Nasdaq Composite recorded 132 new highs and 17 new lows.

Volume on U.S. exchanges was 6.87 billion shares, compared to the 8.07 billion average for the last 20 trading days. (Additional reporting by Ankur Banerjee and Sruthi Shankar in Bengaluru; Editing by Nick Zieminski and James Dalgleish)